$$relation = {(a, b) | b − 3 < a ∧ a < b + 3}$$
Unsure how to proof transitivity. Also is my reflexive and symetric proof strong enough?
A = $\{\mathbb{Z}\}$
Reflexive: yes because $\forall x \in A, (x,x) \in relation.$
Symetric: yes because $\forall x,y \in A, (x,y) \in relation \xrightarrow[]{} (y,x) \in relation$.
Transitive: ?
I know the definition but unsure how to approach the last proof